Infectious disease outbreaks can be responsible for devastating consequences. For example, the 2014-16 Ebola epidemic in west Africa led to more than 11,000 deaths, putting it at the centre of the news agenda. During this talk, using Ebola as a case study, I will discuss how stochastic epidemiological models can be used at different stages of an infectious disease outbreak. At the beginning of an outbreak, key questions include: how can surveillance be performed effectively, and will the outbreak develop into a major epidemic? When a major epidemic is ongoing, decision makers often attempt to forecast the final epidemic size and plan control interventions to reduce the impact of the epidemic. And at the apparent end of an epidemic, an important question is whether the epidemic is really over once there are no new symptomatic cases. Mathematical modelling can be used to address these questions, and is therefore a useful tool for decision makers throughout an outbreak.